Find Reduced Row Echelon Form [[1,h,4],[3,6,8]]

Problem

[[1,h,4],[3,6,8]]

Solution

1. Identify the first pivot in the first row, which is already 1 in the first column.

2. Eliminate the entry below the first pivot by performing the row operation (R_2)→(R_2)−3*(R_1)

[[1,h,4],[3−3*(1),6−3*(h),8−3*(4)]]

[[1,h,4],[0,6−3*h,−4]]

3. Normalize the second row to create the second pivot by dividing (R_2) by 6 - 3h,a*s(s(u))*m*i*n*g - 3h \neq 0$.

(R_2)→1/(6−3*h)*(R_2)

[[1,h,4],[0,1,(−4)/(6−3*h)]]

4. Simplify the fraction in the second row.

(−4)/(6−3*h)=(−4)/(3*(2−h))

[[1,h,4],[0,1,(−4)/(3*(2−h))]]

5. Eliminate the entry above the second pivot by performing the row operation (R_1)→(R_1)−h*(R_2)

[[1,h−h(1),4−h((−4)/(3*(2−h)))],[0,1,(−4)/(3*(2−h))]]

6. Simplify the entry in the first row, third column.

4+(4*h)/(3*(2−h))=(12*(2−h)+4*h)/(3*(2−h))

(24−12*h+4*h)/(3*(2−h))=(24−8*h)/(3*(2−h))

(8*(3−h))/(3*(2−h))

Final Answer

rref*[[1,h,4],[3,6,8]]=[[1,0,(8*(3−h))/(3*(2−h))],[0,1,(−4)/(3*(2−h))]]

Want more problems? Check here!